The DP-32SD has a "Clear All Record Buttons" button where the CD button used to be.
Functionally, I'd guess based on Phil's videos that they are the same. I haven't found any variances between his DP-32SD videos and my DP-24 functions (except for the mono/stereo track option, of course).

I'm only guessing, but likely not the same firmware. If for no other reason, different screens for MIDI and CD, and Mastering (had NSD option for CD) in original not needed in 32SD, and the aforementioned new button. One of the cool things with the original units is the MIDI port could be used to join two boards to work in sync (or so my manual says, anyway).